Usually the easiest way is to use a prefab which get attached to the affected unit as long as it doesn't have one yet. This effect-prefab will take care of your effect (particle system, ...) and will destroy itself after a certain amount of time. This time should be "retriggerable". So each time the effect caster does it's check it does the following:

Check if the unit already has the prefab attached

If it has, retrigger the timeout

if not, create an instance of the prefab and attach it as child to the unit.

I wouldn't use Update in this case. It's usually enough to do this check every 0.5 seconds or every 0.1 if you want. The timeout should be at least double this interval time, so it never runs out while the unit is inside the affected range.

To check if the prefab is already attached you can use GetComponentInChildren with the script type that's part of your prefab. If it has one you can use the returned reference to retrigger the script, if not, create the prefab.